Review for Test #2- Derivatives Rules, Implicit, Related

What is dy/dx?

 $y=2\ln\left(3-x\right)$  

•  $\frac{2}{3-x}$  

•  $\frac{-2}{3-x}$  

•  $\frac{1}{3-x}$  

•  $3-x$  

What is dy/dx? 

 $y^3=6x$  

•  $\frac{2}{y^2}$  

•  $\frac{3}{y^3}$  

•  $3y^2$  

•  $\frac{2x}{y^2}$  

Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?

• 3 ft/sec
• -7.2 ft/sec
• 7.2 ft/sec
• 12

Tags

CCSS.8.G.B.8

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Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The radius of the spill increases at a rate of 5 m/min. How fast is the area of the spill increasing when the radius is 5 m?

• 50π m²/min

• 47π m²/min

• 52π m²/min

• 40π m²/min

Tags

CCSS.7.G.B.4

A spherical snowball melts so that its radius decreases at a rate of 4 in/sec. At what rate is the volume of the snowball changing when the radius is 4 in?

• -262π in³/sec

• -247π in³/sec

• -256π in³/sec

• -263π in³/sec

Tags

CCSS.8.G.C.9

CCSS.HSG.GMD.A.3

A 5 ft ladder is leaning against a wall and sliding towards the floor. The top of the ladder is sliding down the wall at a rate of 2 ft/sec. How fast is the base of the ladder sliding away from the wall when the base of the ladder is 3 ft from the wall?

• 4/3 ft/sec

• 8/7 ft/sec

• 1 ft/sec

• 8/3 ft/sec

Tags

CCSS.8.G.B.8

Find dy/dx at the given point

x³ +2xy -y²=11 at (2,3)

• -4/7

• 12

• -9

• 9

find y' for y= sin(2x²)

• 4sin(2x²)

• 4xcos(2x²)

• 2xcos(2x²)

• xcos(4x²)

An equation of the line tangent to the graph of

 $g\left(x\right)=\frac{3}{x^2+2}$  when  $x=-1$ is

•  $y=\frac{-2}{3}\left(x+1\right)-1$  

•  $y=\frac{-2}{3}\left(x-1\right)+1$  

•  $y=\frac{2}{3}\left(x+1\right)+1$  

•  $y=\frac{2}{3}\left(x-1\right)+1$